Georgia Department of Education
Effective Instructional Practices Guide
Mathematics Effective Instructional Practices
Richard Woods, State School Superintendent
Three-Act Tasks: Step-by-Step “Cheatsheet”
3-Acts and Patient Problem Solving (Teaching without the Textbook)
Adapted from Dan Meyer
Developing the mathematical Big Idea behind the 3-Act task:
• Create or find/use a clear visual which tells a brief, perplexing mathematical story. Video or live
action works best. (See resource suggestions in the Guide to 3-Act Tasks)
• Video/visual should be real life and allow students to see the situation unfolding.
• Remove the initial literacy/mathematics concerns. Make as few language and/or math
demands on students as possible. You are posing a mathematical question without words.
• The visual/video should inspire curiosity or perplexity which will be resolved via the
mathematical big idea(s) used by students to answer their questions. You are creating an
intellectual need or cognitive dissonance in students.
Enacting the 3-Act in the Classroom
Act 1 (The Question):
Set up student curiosity by sharing a scenario:
• Teacher says, “I’m going show you something I came across and found interesting” or,
“Watch this.”
• Show video/visual.
• Teacher asks, “What do you notice/wonder?” and “What are the first questions that come
to mind?”
• Students share observations/questions with a partner first, then with the class (Think-Pair-
Share). Students have ownership of the questions because they posed them.
• Leave no student out of this questioning. Every student should have access to the scenario.
No language or mathematical barriers. Low barrier to entry.
• Teacher records questions (on chart paper or digitally-visible to class) and ranks them by
popularity.
• Determine which question(s) will be immediately pursued by the class. If you have a
particular question in mind, and it isn’t posed by students, you may have to do some skillful
prompting to orient their question to serve the mathematical end. However, a good video
should naturally lead to the question you hope they’ll ask. You may wish to pilot your video
on colleagues before showing it to students. If they don’t ask the question you are after,
your video may need some work.
• Teacher asks for estimated answers in response to the question(s). Ask first for best
estimates, then request estimates which are too high and too low. Students are no defining
and defending parameters for making sense of forthcoming answers.
• Teacher asks students to record their actual estimation for future reference.
Act 2 (Information Gathering):
Georgia Department of Education
Effective Instructional Practices Guide
Mathematics Effective Instructional Practices
Richard Woods, State School Superintendent
Students gather information, draw on mathematical knowledge, understanding, and resources to
answer the big question(s) from Act-1:
• Teacher asks, “What information do you need to answer our main question?”
• Students think of the important information they will need to answer their questions.
• Ask, “What mathematical tools do you have already at your disposal which would be useful
in answering this question?”
• What mathematical tools might be useful which students don’t already have? Help them
develop those.
• Teacher offers smaller examples and asks probing questions.
o What are you doing?
o Why are you doing that?
o What would happen if…?
o Are you sure? How do you know?
Act 3 (The Reveal):
The payoff.
• Teacher shows the answer and validates students’ solutions/answer.
• Teacher revisits estimates and determines closest estimate.
• Teacher compares techniques, and allows students to determine which is most efficient.
The Sequel:
• Students/teacher generalize the math to any case, and “algebrafy” the problem.
• Teacher poses an extension problem- best chance of student engagement if this extension
connects to one of the many questions posed by students which were not the focus of Act
2, or is related to class discussion generated during Act 2.
• Teacher revisits or reintroduces student questions that were not addressed in Act 2.
Georgia Department of Education
Effective Instructional Practices Guide
Mathematics Effective Instructional Practices
Richard Woods, State School Superintendent
Choosing a Three-Act Task
A Three-Act Task may stand alone, introduce new content, or may be a part of a series of related mathematical
tasks which share or develop connections among mathematical ideas.
Three-Act Tasks- Defining Features
The chart below outlines some of the features of a Three-Act Task which distinguish it from other mathematical
tasks.
Facilitation Feature
Student Experience
Problems are presented without
structure
• Students develop questions to be explored
• Students develop the manner in which mathematics will be
used to model the situation presented in the problem
Teacher scribes the questions asked by
students during Act One
• Multiple questions are made public
• Students see multiple mathematical possibilities for
exploration taken from a single context
• Students feel ownership of the questions rather than being
shown a question and solution path
Estimations are expected prior to
beginning to solve the problem
•
Students learn to make conjectures
• Students develop the ability to determine the reasonableness
of answers
All answers are shared and discussed
•
Every student has the opportunity to share his/her way of
approaching, thinking about, and solving the problem
• Mistakes and misconceptions surface and are treated as
learning opportunities
• Students examine and critique the reasoning of others
Teacher guides the flow of the Three-
Act through skillful questioning,
creating questions that lead to student
thinking and respond to student
thinking
• Students have the opportunity to explore the math rather
than simply find the answer
• Students develop deep understanding of the mathematics
and create connections to known mathematical ideas
